On some mathematical aspects of data protection in cloud computing

The talk is dedicated to ideas of Holomorphic Encryption and Multivariate Key Dependent Cryptography. We observe recent theoretical results on the mentioned above topics together with their Applications to Cloud Security. Post Quantum Cryptography could not use many security tools based on Number Theory, because of the factorization algorithm developed by Peter Shor. This fact and fast development of Computer algebra make multivariate cryptography an important direction of research. The idea of key dependent cryptography looks promising for applications in Clouds, because the size of the key allows to control the speed of execution and security level. We will discuss recent results on key dependent multivariate cryptography. Finally, special classes of finite rings turned out to be very useful in holomorphic encryption and for the development of multivariate key dependent algorithms.